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Researcher profile

Olaf Hohm

Olaf Hohm contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
hep-thmath-phmath.MPgr-qccond-mat.dis-nnMachine Learning

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Published work

13 published item(s)

preprint2026arXiv

Color-kinematics duality from an algebra of superforms

Color-kinematics duality states that the kinematic numerators of the cubic tree-level Yang-Mills scattering amplitudes obey the same symmetry properties that the color factors obey due to the Jacobi identity. We present a novel strategy for deriving this duality, based on the differential forms on a superspace. This space of superforms carries a generalization of a Batalin-Vilkovisky (BV) algebra (BV$^{\square}$ algebra). We show that the homotopy algebra of color-stripped Yang-Mills theory is obtained as a quotient of this space in which a subspace, which is an ideal `up to homotopy', is modded out. This algebra is a subsector of a BV$_{\infty}^{\square}$ algebra. Deriving the latter would provide a first-principle proof of color-kinematics duality from field theory.

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preprint2026arXiv

Lecture Notes on Statistical Physics and Neural Networks

These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the goal of making concepts such as phase transitions and the renormalization group accessible to readers without prior knowledge of physics. We introduce the Boltzmann-Gibbs distribution and the thermodynamic potentials on a finite configuration space, notably for Ising spins and spin-glass models on a lattice, and then define phase transitions as discontinuities that arise in the limit that the number of lattice points goes to infinity. We further introduce Hopfield networks and Boltzmann machines, which are governed by the same energy function as spin-glass models, and discuss the learning algorithm for restricted Boltzmann machines. In this algorithm hidden neurons are integrated out as in the renormalization group. Finally, modern deep learning is introduced, whose early developments were in part motivated by restricted Boltzmann machines in that they carry many layers of hidden neurons. A description of large language models is given.

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preprint2022arXiv

Double Field Theory as the Double Copy of Yang-Mills

We show that double field theory arises from the color-kinematic double copy of Yang-Mills theory. A precise double copy prescription for the Yang-Mills action at quadratic and cubic order is provided that yields the double field theory action in which the duality invariant dilaton has been integrated out. More precisely, at quadratic order this yields the gauge invariant double field theory, while at cubic order it yields the cubic double field theory action subject to a gauge condition that originates from Siegel gauge in string field theory.

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preprint2022arXiv

Duality invariant string beta functions at two loops

We compute, for cosmological backgrounds, the $O(d,d;\mathbb{R})$ invariant beta functions for the sigma model of the bosonic string at two loops. This yields an independent first-principle derivation of the order $α'$ corrections to the cosmological target-space equations. To this end we revisit the quantum consistency of Tseytlin's duality invariant formulation of the worldsheet theory. While we confirm the absence of gravitational (and hence Lorentz) anomalies, our results show that the minimal subtraction scheme is not applicable, implying significant technical complications at higher loops. To circumvent these we then change gears and use the Polyakov action for cosmological backgrounds, applying a suitable perturbation scheme that, although not $O(d,d;\mathbb{R})$ invariant, allows one to efficiently determine the $O(d,d;\mathbb{R})$ invariant beta functions.

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preprint2022arXiv

Supersymmetric action for 6D $(4,0)$ supergravity

We give a linearized but otherwise complete supersymmetric action for ${\cal N}=(4,0)$ supergravity in six dimensions, using a Kaluza-Klein-type $5+1$ split of coordinates and fields. We provide in particular a significantly simplified version of the bosonic action derived by us recently. This formulation employs fields that are no longer irreducible, subject to a local Lorentz invariance, which in turn simplifies the supersymmetry transformations including the exotic gravitino.

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preprint2022arXiv

The Gauge Structure of Double Field Theory follows from Yang-Mills Theory

We show that to cubic order double field theory is encoded in Yang-Mills theory. To this end we use algebraic structures from string field theory as follows: The $L_{\infty}$-algebra of Yang-Mills theory is the tensor product ${\cal K}\otimes \mathfrak{g}$ of the Lie algebra $\mathfrak{g}$ of the gauge group and a `kinematic algebra' ${\cal K}$ that is a $C_{\infty}$-algebra. This structure induces a cubic truncation of an $L_{\infty}$-algebra on the subspace of level-matched states of the tensor product ${\cal K}\otimes \bar{\cal K}$ of two copies of the kinematic algebra. This $L_{\infty}$-algebra encodes double field theory. More precisely, this construction relies on a particular form of the Yang-Mills $L_{\infty}$-algebra following from string field theory or from the quantization of a suitable worldline theory.

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preprint2021arXiv

Gauge Invariant Perturbation Theory via Homotopy Transfer

We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.

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preprint2020arXiv

Duality Invariance and Higher Derivatives

We dimensionally reduce the spacetime action of bosonic string theory, and that of the bosonic sector of heterotic string theory after truncating the Yang-Mills gauge fields, on a $d$-dimensional torus including all higher-derivative corrections to first order in $α'$. A systematic procedure is developed that brings this action into a minimal form in which all fields except the metric carry only first order derivatives. This action is shown to be invariant under ${\rm O}(d,d,\mathbb{R})$ transformations that acquire $α'$-corrections through a Green-Schwarz type mechanism. We prove that, up to a global pre-factor, the first order $α'$-corrections are uniquely determined by ${\rm O}(d,d,\mathbb{R})$ invariance.

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preprint2020arXiv

Green-Schwarz Mechanism for String Dualities

We determine the complete spacetime action to first order in $α'$ for the massless fields of bosonic string theory compactified on a $d$-dimensional torus. A fully systematic procedure is developed that brings the action into a minimal form in which all fields apart from the metric enter only with first-order derivatives. T-duality implies that this action must have a global $\mathrm{O}(d,d,\mathbb{R})$ symmetry, and we show that this requires a Green-Schwarz type mechanism for $α'$-deformed $\mathrm{O}(d,d,\mathbb{R})$ transformations. In terms of a frame formalism with ${\rm GL}(d)\times {\rm GL}(d)$ gauge symmetry this amounts to a modification of the three-form curvature by a Chern-Simons term for composite gauge fields.

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preprint2020arXiv

Homotopy Transfer and Effective Field Theory I: Tree-level

We use the dictionary between general field theories and strongly homotopy algebras to provide an algebraic formulation of the procedure of integrating out of degrees of freedom in terms of homotopy transfer. This includes more general effective theories in which some massive modes are kept while other modes of a comparable mass scale are integrated out, as first explored by Sen in the context of closed string field theory. We treat $L_\infty$-algebras both in terms of a nilpotent coderivation and, on the dual space, in terms of a nilpotent derivation (corresponding to the BRST charge of the field theory) and provide explicit formulas for homotopy transfer. These are then shown to govern the integrating out of degrees of freedom at tree level, while the generalization to loop level will be explored in a sequel to this paper.

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preprint2020arXiv

Leibniz Gauge Theories and Infinity Structures

We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based on `tensor hierarchies', which describe towers of $p$-form gauge fields transforming under non-abelian gauge symmetries and which have been constructed up to low levels. Here we define `infinity-enhanced Leibniz algebras' that guarantee the existence of consistent tensor hierarchies to arbitrary level. We contrast these algebras with strongly homotopy Lie algebras ($L_{\infty}$ algebras), which can be used to define topological field theories for which all curvatures vanish. Any infinity-enhanced Leibniz algebra carries an associated $L_{\infty}$ algebra, which we discuss.

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preprint2020arXiv

Toward Exotic 6D Supergravities

We investigate exotic supergravity theories in 6D with maximal (4,0) and (3,1) supersymmetry, which were conjectured by C. Hull to exist and to describe strong coupling limits of ${\cal N}=8$ theories in 5D. These theories involve exotic gauge fields with non-standard Young tableaux representations, subject to (self-)duality constraints. We give novel actions in a 5+1 split of coordinates whose field equations reproduce those of the free bosonic (4,0) and (3,1) theory, respectively, including the (self-)duality relations. Evidence is presented for a master exceptional field theory formulation with an extended section constraint that, depending on the solution, produces the (4,0), (3,1) or the conventional (2,2) theory. We comment on the possible construction of a fully non-linear master exceptional field theory.

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preprint2019arXiv

Non-perturbative de Sitter vacua via $α'$ corrections

The higher-derivative $α'$ corrections consistent with $O(d,d)$ duality invariance can be completely classified for cosmological, purely time-dependent backgrounds. This result is used to show that there are duality invariant theories featuring string-frame de Sitter vacua as solutions that are non-perturbative in $α'$, thus suggesting that classical string theory may realize de Sitter solutions in an unexpected fashion.

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